
Jun 26 2012
WITS Node Seminar: Dr Rytis Paškauskas
The National Institute for Theoretical Physics, and the Centre for Theoretical Physics, School of Physics, would like to invite to its coming talk in the theory seminar series, entitled:
"Equilibration in the CurieWeiss anisotropic quantum Heisenberg model"
to be presented by Dr. Rytis Paškauskas (NITheP/Stellenbosch)
Abstract: Equilibration in a quantum spin model with meanfield interactions is explored, following the principle that if sufficiently many ``generic,'' noncommuting observables approach their equilibrium values, then the system as a whole equilibrates. The questions pondered in this talk are: What is the rate of relaxation of a certain class of observables? Are there initial states, perhaps atypical, that have odd dynamical patterns?
In the framework of the quantum BogoliubovBornGreenKirkwoodYvon
(BBGKY) hierarchy, an unconventional representation that is different from the usual cluster expansion is introduced, which casts the hierarchy into the form of a secondorder recursion. This coefficient representation allows to classify all symmetries of the equations of motion for arbitrary coupling parameters of the model: It is found that there are either 2, 4, or O(N) symmetry subspaces, and the coefficient BBGKY hierarchy decouples into the corresponding number of Hermitian Liouville operators on each subspace. The complexity of these Liouvillians does not permit an analytic solution in general. A novel approach of solving the problem is proposed, whereby instead of being numerically diagonalized, the Liouville operator is first tridiagonalized by using the stabilized Lanczos algorithm. As a result, the Green's operator is expressed in terms of a certain orthogonal polynomial sequence with numerically computed coefficients of recursion.
By Fourier transforming their orthogonality weight function, evolution of selected observables may be determined. This approach provides a framework within which more questions about subtleties of this model can be answered in some cases analytically, and in all other cases by a mixture of analytic insights and an efficient computational algorithm that can reach the thermodynamic limit. This methodology does not make the matrix product or other simplifying assumptions about the structure of the density matrix. Nevertheless it appears to be uniquely positioned to provide detailed answers to the aforementioned questions.
Date: Tuesday, 26th June 2012
Venue: Frank Nabarro Lecture Theatre P216
Time: 13.20  14.10
For more information please contact:
Alan S. Cornell
School of Physics
University of the Witwatersrand
Private Bag 3
Wits 2050
South Africa
Tel.:+27117176819
contact
 NITheP Stellenbosch node
 Rene Kotze
National Institute for Theoretical Physics
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Matieland,
Stellenbosch, South Africa,7602  Phone: +27 (0)21 808 2653  Fax: +27 (0)218083862
 NITheP Gauteng node
 Paula Marais
Physical address: University of Witwatersrand
School of Physics
Jan Smuts Avenue
Braamfontein
JHB
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 NITheP KZN node
 Ms Nelisiwe Mncube
National Institute for Theoretical Physics
University of KwaZuluNatal
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Durban
4000
South Africa
 Phone: 27 (0)31 260 7570  Fax: 27 (0)31 260 8090
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